If $X \sim \chi^2$ with $n$ degrees of freedom then how is the distribution of the random variable $-X$? I think that $-X \sim \chi^2$ with $-n$ degrees of freedom but I dont sure.
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I don't know if it's what you're asking, but if $X$ is a random variable with density $f$, then $-X$ is a random variable with density $g$, where $g(x) = f(-x)$ – Presage Oct 11 '20 at 18:15
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In my case how degrees of freedom has -X? – wessi Oct 11 '20 at 18:19
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as J.G mentioned in his answer, we don't really have a name for such distribution, it's not $\chi^2$ in usual sense, so there are no "degrees of freedom" – Presage Oct 11 '20 at 18:40
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Since $X\ge0$, $-X$ cannot have the same distribution. There isn't really a name for the distribution of $-X$; the best we can write is $-X\sim-\chi_n^2$.
J.G.
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